SOLUTION: Simplify the expression (3n+2)!/(3n-3)!

Question 1001515: Simplify the expression
(3n+2)!/(3n-3)!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
(3n+2)! / (3n-3)! = (3n+2)*(3n+1)*(3n)*(3n-1)*(3n-2)*(3n-3)! divided by (3n-3)!

the (3n-3)! in the numerator and denominator cancel out and you are left with:

(3n+2)*(3n+1)*(3n)*(3n-1)*(3n-2)

for example:

let n = 7

3n+2 = 23
3n+1 = 22
3n+0 = 21
3n-1 = 20
3n-2 = 19
3n-3 = 18

(3n+2)! / (3n-3)! = (3n+2)*(3n+1)*(3n)*(3n-1)*(3n-2)*(3n-3)! divided by (3n-3)! which becomes:
23! / 18! = (23 * 22 * 21 * 20 * 19 * 18! divided by 18! which becomes:
(23 * 22 * 21 * 20 * 19)

the result is 4037880

i used my ti-84 to take 23! and divide it by 18! and i got 4037880.

this confirms the solution is correct.

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